UPDATE - Solved
After replacing the Vid card & motherboard, it turned out that I had a faulty PSU. Swapped in another unit and the machine has been working flawlessly ever since.
First, please excuse the potential repost here. I've been searching for an hour, but because TH doesn't have a real forum search, my efforts bore no fruit. I'm also not certain which forum to post this in since there seems to be some redundancy. Mods, feel free to move this - I won't be offended.
Machine does a full power off after 0-10min. All fans turn off, PSU turns off, all LEDs turn off, all drives turn off. After a few moments like this, the machine turns itself back on again and boots.
Symptoms and background:
Sometimes the machine just shuts off
Sometimes the video begins to flicker once or twice, though the time between flicker and power off is not consistent
No temperature LEDs on the motherboard light, indicating that temps for NB and CPU are both below the min require for those LEDs
No temp alarm beep ends up beeping
Vid card heatsink, heatsink mounts, and board surface directly behind GPU are all cool to the touch when this happens
Machine runs just fine when the generic VGA driver is used. This only happens when the ATI driver is used, as far as I can tell
Memtest uncovered nothing
Unfortunately, I don't have any backup parts that I can swap in for troubleshooting
Note: All hardware is brand new other than the HD, which is a fresh pull and known good unit. Also, everything is running at stock speeds using factory coolers and fans.
I tried installing CCC 10.3 with no luck (will update OP to reflect this). Reviews of the card pointed me to a driver which is actually newer than what is included in CCC 10.3, so I'm trying to install that right now. Will post an update if it works.
Yes, you are running two sticks of RAM (dual channel) in a triple channel board (3 sticks). The i7 only supports triple channel memory and that could be the source of your problem. Take a look at the OCZ gold series Triple channel, i7 memory. The only thing is that, triple channel memory comes in 6 and 12 gigs and you will therefore need a 64-bit OS to use all 6 gigs. A 32 bit OS as you have will only use 3 - 3.5 gigs of all physical RAM installed. What im saying is you really should get triple channel memory for the system to run stable but it would not make sense to run 6 gigs of ram when you can only use 3 gigs due to the limitations of the OS.
Currently, you have 4 gigs but ur PC only actually uses 3 - 3.5 gigs of it. Get a 64 bit OS and triple channel memory.
This is obviously a power supply issue, try another power supply. The fact that it only occurs when running the ATI drivers means that this is when the graphics card is drawing the most current. Are you sure that you have connected the 4 pin cable to the motherboard and any required power leads to the graphics card?
Motherboard defaults to driving it at 1.52V for some reason. Both modules check in like this, but Windows only lists one of them as "usable". With the voltage set to 1.66V, there appears to be no difference in stability and only 2.00GB shows as usable (although 4GB shows as installed).
There was a moment where both DIMMs were listed as usable (3.50GB), and that definitely improved my benchmark, but the machine still powered off as usual.